Finite Element Simulation of the Response of No-Tension Materials
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Unbound granular materials that are used at base layer of flexible pavement cannot resist tensile forces. These materials are called no-tension materials. In this paper, a modified strain-energy function was used to describe the constitutive behavior of granular materials to simulate flexible pavement within the finite element framework CAPA3D .The constitutive model was defined such that the positive stresses in principal directions were zero. Comparisons between the no-tension materials and linear elastic materials for different boundary conditions and geometries were presented in this paper. The results of FE analysis show that effect of using no-tension model for base layer on pavement performance is significant. The deformation at top and horizontal strain at the bottom of asphalt concrete layer are higher when the no-tension model is used.
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Finite Element Simulation of the Response of No-Tension Materials
- 1. Finite Element Simulation of the Response of No-Tension Materials Alieh Alipour & Tom Scarpas Delft University of Technology Section of Pavement Engineering
- 2. Alieh Alipour & Tom Scarpas Simulation No-Tension characteristics of aggregates No-Tension Materials Prediction pavement performance
- 3. Decreasing load-induced stress transferred to subgrade Providing support for the surface layer Drainage Protection subgrade against frost Unbound aggregates (Base & Subbase Layer)
- 4. Alieh Alipour & Tom Scarpas Unbound aggregates modelling (FEM) Cross- anisotropic Different Horizontal and vertical moduli Not suitable for thin AC layer Unable to predict the nonlinear & stress dependent response of aggregates Wrong prediction of tensile stresses at bottom of base layer Linear isotropic elastic model Nonlinear Stress dependent response Different Horizontal & vertical moduli Difficulties in determining anisotropic material properties Nonlinear cross anisotropic model No-tension Model
- 5. Alieh Alipour & Tom Scarpas Constitutive Model: Modified Hook’s Law 1D
- 6. Alieh Alipour & Tom Scarpas Principal Strains Strain Constitutive Model: Principal Strains
- 7. Alieh Alipour & Tom Scarpas Constitutive Model: Special Operator Special Operator
- 8. Alieh Alipour & Tom Scarpas Constitutive Model: Special Operator Special Operator
- 9. Alieh Alipour & Tom Scarpas Constitutive Model: Strain energy function removal of the stiffness & stress along principal tensile strain direction
- 10. Alieh Alipour & Tom Scarpas Principal Stresses Stresses Constitutive Model: Principal Stresses
- 11. Alieh Alipour & Tom Scarpas Tangent Moduli Constitutive Model: Implementing in FEM Stresses FEM
- 12. Alieh Alipour & Tom Scarpas (a) (b) Validation of the Model No-Tension Hyperelastic Horizontalstrain Time (sec)
- 13. Alieh Alipour & Tom Scarpas Tire Horizontal strain Compressive strain AC layer Base layer Material Type Model E (MPa) Poisson’s ratio AC layer Hyperelastic Material 3500 0.35 Base Hyperelastic Material 600 0.35 Base No-tension Material 600 0.35 Results of Flexible Pavement Simulation
- 14. Alieh Alipour & Tom Scarpas Results of Flexible Pavement Simulation Hyperelastic material No-Tension material
- 15. Alieh Alipour & Tom Scarpas Results: Deflection of AC layer No-Tension Hyperelastic Deflection(mm) Distance from CL ( mm)
- 16. Alieh Alipour & Tom Scarpas Results: Horizontal Strain (bottom of AC layer) No-Tension Hyperelastic Horizontalstrain Distance from CL ( mm)
- 17. Alieh Alipour & Tom Scarpas Results: Vertical strain (top of base layer) No-Tension Hyperelastic Verticalstrain Distance from CL ( mm)
- 18. Alieh Alipour & Tom Scarpas Results: Effect of Poisson’s ratioDeflection(mm) Distance from CL ( mm) Poisson’s ratio=0.1 Poisson’s ratio=0.35 Poisson’s ratio=0.45
- 19. Alieh Alipour & Tom Scarpas Results: State of stress (Base Layer)StressinYdirection Distance from CL ( mm) No-tension Y=1450 mm Hyperelastic Y=1450 mm No-tension Y=1350 mm Hyperelastic Y=1350 mm
- 20. Alieh Alipour & Tom Scarpas Conclusion No-Tension Material Model is implemented in FEM. Effect of using no-tension model for base layer on pavement performance is significant. The deformation at top and horizontal strain at bottom of AC layer are higher when no-tension model is used. No-Tension Material Model is sensitive to Poisson’s ratio.
- 21. Alieh Alipour & Tom Scarpas Delft University of Technology Section of Pavement Engineering Thank You for Your Attention!
Editor's Notes
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- A flexible pavement structure is typically composed of several layers of material. Each layer receives the loads from the above layer, spreads them out, then passes on these loads to the next layer below. Typical flexible pavement structure consists of: Surface layer. This is the top layer and the layer that comes in contact with traffic. Base layer. This is the layer directly below the surface course and generally consists of aggregates (either stabilized or unstabilized) Subbase layer. This is the layer (or layers) under the base layer. The unbound granular layer serves as major structural component in flexible pavements, especially when the hot mix asphalt (HMA) surface is thin. Unbound granular materials that are used at base layer of flexible pavement cannot resist tensile forces. these materials are called no-tension materials. The accurate prediction of pavement performance
- Unbound aggregate base is a primary structural layer of a pavement.
- The studies show that UAB should be modeled as nonlinear and cross-anisotropic to account for stress sensitivity and the significant differences between vertical and horizontal moduli and Poisson’s ratios. The advantage of the use of cross-anisotropy for the analysis of unbound granular bases is the drastic reduction of bottom tensile strain predicted by linear elastic analysis based on the assumptions of isotropy. An alternative to the use of anisotrpic plasticity and nonlinear analysis techniques is the simulation of the low tensile response characteristics of granular materials by means of what is known as no-tension models. The objective of this study is the evaluation of the contribution on the overall pavement response by use of No-tension model.
- The perfectly no-tension material model assumes an idealized continuum made up of granules incapable of sustaining any tensile stress between them, while the material can sustain compressive stresses. Consider a uniaxial compression-tension test in which Hooke’s law describes the uniaxial stress-strain relationship. Sigma=kepsilon Consider a case where a displacement (delta l ) is imposed on a grain chain of unbound aggregates.
- The constitutive law is adjusted such that in principal space the material does not resist against tension.
- A hyperelastic material model is modified such that in compression the material behaves like a normal hyperelastic while in tension the tensile stresses are always zero. The net effect of above choices is the removal of the stiffness and corresponding stress values along tensile principal strain material directions.
- The response of a cube was compared for a no-tension material and hyperelastic material. A linearly increasing uniform pressure with a magnitude of 0,02 Mpa in Y direction and 0,04 Mpa in Z direction was applied on a cube whose faces in the XZ XY and YZ planes were restrained against motion in Y Z and X direction. The material demonstrates much more flexible response than a standard hyperelastic material.
- To understand the effect of granular base simulated as a no-tension material on pavement performance response, a two layer mesh was created and implemented into FE Package. The material properties which were chosen are shown in this table. Lame’s constants are were calculated based on E and Poisson's ratio for the strain energy function and its derivatives. The AC top layer with tickness of 150 mm was simulated as hyperelastic while the second layer was specified in one case as a no-tension material model and in another as hyperelastic. BC: The structure was restrained at the bottom of mesh to avoid movement along the X, Y, and Z directions. Furthermore it was restricted on the Y-Z and the Y-X planes to avoid movement along the X and the Z direction. Load:
- The 3 dimensional states of stress over the height of AC and base layer is plotted at the peak load. As it can be seen the pavement deforms more when the base layer is modeled by no-tension model.
- This figure shows the pavement surface deflection for 2 different base layer material models. As it is shown, when the material properties are specified as no-tension, the deflection of AC layer is almost 1.3 times higher than the case in which base layer was modelled by a hyperelastic model.
- A sensitivity analysis on the effect of Poisson’s ratio on the pavement surface vertical deflection was carried out considering the base layer as a no-tension material. The results are plotted here and it can be seen that as Poisson’s ratio increases, the vertical deflections of the pavement surfaces increases as well.
- Here the distribution of compressive stresses at two different depth within the base layer along the horizontal axis are compared for the no-tension and hyperelastic models in presence of only one wheel. It can be seen that the compression stresses in the base layer slightly higher values for the hyperelastic model compared to the no-tension model.
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